Question

the pythagorean theorem, ( a^2 + b^2 = c^2 ), can be used to determine the lengths of the sides of a right triangle. if leg ( a = 5 ) cm, and leg ( b = 6 ) cm, which of the following equations can be used to determine the length of side ( c )? reference sheet images of geometric formulas/diagrams ( 2(5) + 2(6) = c ) ( (2 + 5) + (2 + 6) = c ) ( sqrt{5^2 + 6^2} = c ) ( 5 + 6 = c )

Explanation:

Step1: Recall Pythagorean Theorem

The Pythagorean Theorem is \(a^2 + b^2 = c^2\) for a right triangle, where \(a\) and \(b\) are legs, \(c\) is the hypotenuse.

Step2: Solve for \(c\)

To find \(c\), take the square root of both sides of \(a^2 + b^2 = c^2\). Substituting \(a = 5\) and \(b = 6\), we get \(c=\sqrt{5^2 + 6^2}\).

Answer:

\(\sqrt{5^2 + 6^2} = c\) (the third option)